Final answer:
To find the other number when the GCD is 11, the LCM is 330, and one number is 66, you multiply the GCD and LCM to get the product of the two numbers (3630) and divide by the given number (66), resulting in the other number being 55.
Step-by-step explanation:
The question involves finding a missing number when the GCD (Greatest Common Divisor) and LCM (Least Common Multiple) of two numbers are known, and one of the numbers is given. The GCD of the two numbers is 11, and their LCM is 330. If one number is 66, we can find the other number using the relationship between the product of two numbers, their GCD, and LCM:
Product of two numbers = GCD × LCM
Here, the product of the two numbers would be 11 × 330. To find the missing number:
- Calculate the product: 11 × 330 = 3630.
- Divide the product by the given number (66) to find the other number: 3630 / 66 = 55.
Therefore, the other number is 55.